Method, a system and a computer program product for determining a beat-to-beat stroke volume and/or a cardiac output

ABSTRACT

The invention relates to a method  10  for determining a beat-to-beat stroke volume  9   a  and/or a cardiac output  9   b  based on a measurement  2  of suitable arterial pressure data. At the step  4  a waveform of the arterial pressure pulse is assessed based on data obtained during the measurement of step  2.  At step  6  a compliance or impedance in dependence of at least one measurement of arterial pressure data is computed using a non-linear model  7.  The non-linear model may comprise an arctangent model. The arctangent model may be differentiated numerically or analytically to obtain the compliance or the impedance of an aortic portions. The thus obtained compliance or impedance may then be substituted into a linear model  8.  The linear model  8  may comprise a Windkessel model  8   a,  or a Waterhammer model  8   b  or any other suitable linear pulse contour model  8   c.  As a result, the beat-to-beat stroke volume  9   a  and/or cardiac output  9   b  are computed.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.12/669,890, filed Apr. 29, 2010, and claims benefit of NetherlandApplication No. PCT/NL2007/050362, filed Jul. 20, 2007, and herebyincorporated by reference herein.

FIELD OF THE INVENTION

The invention relates to a method for determining a beat-to-beat strokevolume and/or a cardiac output based on at least one measurement, of anarterial pressure data.

The invention further relates to a computer program product fordetermining a beat-to-beat stroke volume and/or cardiac output based onat least one measurement of an arterial pressure data.

The invention still further relates to a system for determining abeat-to-beat stroke volume and/or a cardiac output based on at least onemeasurement of an arterial pressure data.

BACKGROUND OF THE INVENTION

Blood pressure and cardiac output, or pressure and flow, respectively,in the aorta of a patient, define its hemodynamic state. Thishemodynamic state may change on a short time scale of seconds andminutes requiring continuous or semi-continuous monitoring. Thus,instrumentation has been developed for over a century for measuring bothblood pressure and flow on a continuous basis. Unfortunately, themeasurement of cardiac output (i.e. flow) is almost impossible toperform in a safe and continuous way. In contrast, blood pressure can bemeasured in patients on a continuous basis by invasive means with alittle risk, but not entirely without risk, and more recently alsonon-invasively with the per se known Finapres methodology. Hence, thereis a need for a method to derive flow from pressure using a computationinstead of a measurement.

When recording pulsatile blood pressure and flow simultaneously inexperimental animals, it was observed that if flow went up so did bloodpressure and when flow went down blood pressure went down. Bothhemodynamic signals are thus coupled. From physics and engineering oneknows that pressure and flow are related via an impedance: p=q Z, with ppressure, q flow, and Z impedance. The proper impedance to relate aorticflow to aortic pressure is referred to as aortic impedance. But it ishard if not impossible to determine the aortic impedance in anindividual patient. In principle, the impedance can be derived from thepressure flow as

Z=p/q

but the flow (q) cannot be measured easily as a waveform. A possibleapproach is the use of suitable models.

Windkessel Model

The oldest model for the hemodynamic properties of the aorta is theso-called “Windkessel” model. The equation to compute a stroke volumefrom the contour of the pressure pulse according to the Windkessel modelis as follows:

Vs=C(p2−p1)(1+As/Ad)

with Vs—a stroke volume, C—an aortic compliance defined as dV/dP, p2—apressure at a dicrotic notch, p1 the diastolic pressure, As theintegrated area under the systolic portion of the blood pressure curve,and Ad similarly the diastolic area. The dicrotic notch is a pulse thatprecedes a dicrotic wave, it being a pulse sequence comprising adouble-beat sequence wherein a second beat is weaker than a first beat.It is a disadvantage of this model that the compliance C of the aortamust be known. In practice the compliance is an unknown variable. In theprior art, the compliance has been determined indirectly by calibratingthis value. To this purpose, a cardiac output has been measured with astandard clinical technique such as Fick or indicator dilution, Qi. Astroke volume from an indicator dilution, Vsi, follows as Vsi=Qi/f, withf being the heart rate. The compliance C now follows as the ratioC=Vsi/Vs (C=1). Once calibrated, the method can be used to followchanges and trends in stroke volume, for monitoring purposes.

However, this method has been shown to be unreliable. Various studieshave been performed in which the compliance has been calibrated,followed by administrating of a vasoactive drug to change bloodpressure, heart rate and cardiac output. It appeared that the complianceC changed with the drugs given, in various directions. This yielded thatthe Windkessel method might not be useful in practice.

Uniform Tube or Waterhammer Model

Another hemodynamic model of the aorta is the uniform tube withcharacteristic impedance, or Zc model. It describes the relation betweenpulsatile p(t) pressure and pulsatile flow q(t) in a uniform tube, whileignoring any mean pressure component:

q(t)=p(t)/Zc

with q(t) the pulsatile flow waveform, p(t) pulsatile pressure, and Zcthe aortic characteristic impedance. Integrating the pulsatile signalsfrom diastolic pressure, pd, during systole (when blood is ejected fromthe heart) one obtains:

Vs=1/Zc∫(p(t)−pd)dt

In this equation, the impedance Zc is unknown and can only be determinedwith an individual patient by calibration with a clinical cardiac outputmethod, as described above for the Windkessel method. When tested underthe same circumstances as the Windkessel method, described above,Waterhammer method also appeared unreliable although to a lesser degree,since Zc can be written as:

Zc=√(r/(AC′))

with r the density of blood, A the aortic cross-sectional area and C′the compliance per unit length. When A increases, C′ decreases renderingtheir product and thus impedance Zc relatively constant.

SUMMARY OF THE INVENTION

It is an object of the invention to provide a reliable method fordetermining a beat-to-beat stroke volume and/or a cardiac output basedon at least one measurement of an arterial pressure data.

To this end a method according to the invention comprises the steps of

-   computing a compliance or impedance in dependence of at least one    measurement of arterial pressure data using a non-linear model;-   using said compliance or impedance in a pulse contour method for    determining the beat-to-beat stroke volume and/or cardiac output    based on the measured arterial pressure data.

It is noted that the cardiac output equals the stroke volume multipliedby a heart beat frequency. A method according to the invention can bebased on the insight that a per se known linear pulse contour method,like Windkessel or Waterhammer method, can be improved if respectivevalues of pressure dependence of compliance and impedance that areobtained from a suitable non-linear model are incorporated in theselinear models. A suitable example of a non-linear model is the per seknown aortic arctangent model.

The Aortic Arctangent Model

The aortic mechanical properties of post mortem segments of the thoracicaorta of humans have been measured in vitro over the entirephysiological pressure range. The responses of the internalcross-sectional area of the aorta to an increase in pressure could befitted closely by an arctangent:

A(p)=Am(0.5+(1/π) arctan ((p−p0)/p1))   (1)

in which:

-   A is the cross-sectional area in cm²;-   Am is the maximal area at very high pressure;-   p0 indicates the inflexion point of a pressure curve;-   p1 indicates a halfwidth of a pressure pulse.

For implementing a method of the invention for the arterial pressuredata a pressure waveform may preferably be selected.

In addition, a method according to the invention can be based on furtherinsights and assumptions:

1) the total aortic mechanical properties can be described by themultiplication of the thoracic segment area by an “effective length” Le:

V(p)=A(p)Le   (2)

with V(P) the pressure dependent volume of the aorta. It is assumed thatproperties of the thoracic aorta are representative for the entirelength of the aorta. This assumption is advantageous as it simplifiesthe model to a great extent. Preferably, the effective length of theaorta is about 0.5 a height of the person. Due to this assumption afurther simplification of the model can be obtained.2) the parameters Am, p0 and p1 of the arctangent model are linearlydependent on gender and age of the patient. It has been empiricallyproven that this assumption substantially holds for p0, and isreasonably correct for p1. Thus, given the two well known properties ofa patient—gender and age, the individual physiological scatter in theaortic parameters p0 and p1 can be reduced substantially. In order toimprove accuracy in approximating the maximal area Am at very highpressure, a one-time calibration may be necessary. This improvescomputation accuracy for determining the stroke volume and/or thecardiac output even further.3) a viscous component of the aortic mechanical properties is ignored. Acorresponding pure elastic compliance then follows from differentiatingthe equation for the pressure-dependent cross-sectional area A(p) withrespect to pressure, yielding:

C(p)=Cm/(1+((p−p0)/p1)²)   (3)

with

Cm=Am/(πp1)

wherein

-   C(p) is a pressure-dependent compliance;-   Cm is a maximum compliance of the aortic portion.

The above equations (1)-(3) for cross-sectional area, volume andcompliance of the aorta (and thus also for characteristic impedance) areapplicable to any of the known pulse contour models yielding an improvedmethod for determining the beat-to-beat stroke volume and/or the cardiacoutput based on at least one measurement of an arterial pressure data,notably the waveform. The operation of a method according to theinvention and further advantageous embodiments thereof will be discussedwith reference to FIG. 1. Further advantageous embodiments of a methodaccording to the invention are set forth in the claims.

The computer program product according to the invention comprisesinstructions for causing a processor to carry out the steps of a methodas is set forth in the foregoing. The operation of the computer programwill be discussed in more detail with reference to FIG. 2.

A system according to the invention comprises:

a processing unit arranged for:

-   computing a compliance or impedance in dependence of at least one    measurement of arterial pressure data using a non-linear model;-   using said compliance or impedance in a pulse contour method for    determining a beat-to-beat stroke volume and/or cardiac output based    on the measured arterial pressure data.

The operation of a system according to the invention will be discussedin more detail with reference to FIG. 3. FIG. 4, presents a preferredembodiment of a non-invasive measurement sensor arrangement for use in asystem of FIG. 3.

These and other aspects of the invention will be discussed in moredetail with reference to the figures.

BRIEF DESCRIPTION

FIG. 1 presents a schematic view of an embodiment of a method accordingto the invention.

FIG. 2 presents in a schematic way an embodiment of a flow-chart of acomputer program according to the invention.

FIG. 3 presents a schematic view of an embodiment of a system accordingto the invention.

FIG. 4 presents a schematic view of an embodiment of a cuff for use in asystem of FIG. 3.

It is noted that common parts are identified with common referencenumerals. It is further noted that figures and description thereof areillustrative, not limiting, whereas a combination of details discussedwith reference to different figures is contemplated as well. FIG. 1presents a schematic view of an embodiment of a method according to theinvention. A method 10 according to the invention is arranged fordetermining a beat-to-beat stroke volume 9 a and/or a cardiac output 9 bbased on a measurement 2 of suitable arterial pressure data, notably anarterial pressure waveform. It is noted that for purposes of saidmeasurement any per se known suitable invasive or non-invasive systemmay be used. Preferably, a system as is discussed with reference to FIG.3 or FIG. 4 is used. At the step 4 a waveform of the arterial pressurepulse assessed based on data obtained during the measurement of step 2.At step 6, a compliance or impedance in dependence of at least onemeasurement of arterial pressure data is computed using a non-linearmodel. Preferably, equation (1) as is discussed above may be used forsaid computation, which may be accessed at step 7 of the method 10. Thenon-linear model may comprise an arctangent model. The arctangent modelmay be differentiated numerically or analytically to obtain thecompliance or the impedance of an aortic portion. The thus obtainedcompliance or impedance may then be substituted into a linear model 8.The linear model 8 may comprise a Windkessel model 8 a, or a Waterhammermodel 8 b or any other suitable linear pulse contour model 8 c.

It is noted that the aortic arctangent model has never been earlierincorporated into a linear pulse contour model. Moreover, there havebeen no suggestions that an improvement of a calculation of a strokevolume and/or a cardiac output can be reached if the arctangent modulewere incorporated therein.

It is found to be advantageous to calculate the beat-to-beat strokevolume or the cardiac output based on a total effective aorticcompliance. The total aortic compliance may be described by abeat-to-beat compliance per unit length of the aorta and an effectivelength of the aorta dependent on the person-specific characteristic.Preferably, a height of the person is selected for the person-specificcharacteristic, the effective length of the aorta being given bypreferably Le=0.5*H, wherein H is height of the person. More preferably,a heart rate dependent model is included in a computational model. Thismay be achieved by computing the aortic compliance for an effectivepressure. Preferably, a mean pressure during systole is selected, whichmay be calculated based on a beat-to-beat pressure for a contractionfrequency of the heart. Due to incorporation of the heart rate dependentmodel into computation of the beat-to-beat stroke volume or the cardiacoutput, a further improvement of computational accuracy is achieved.

When the non-linear model (1) is applied to the Windkessel model oneobtains:

Vs=C(p)(p2−p3)(1+As/Ad),

wherein

-   Vs is a stroke volume;-   C(p) is an aortic compliance;-   p2 is a pressure at a dicrotic notch;-   p3 is a diastolic pressure,-   As is an integrated area under a systolic portion of a blood    pressure curve;-   Ad is an integrated area under a diastolic portion of a blood    pressure curve.

It is found that major improvement in the reliability of the Windkesselmethod may be achieved if the compliance C(p) is assumed constant foreach beat and its value is obtained from the equation (3) for C(p) at afixed, so-called “effective” pressure level, pe, for that beat. Hence,the C is replaced by a C(pe), with pe to be determined from the measuredarterial pressure data.

Due to the fact that the cross-sectional area of the aorta is beingapproximated by the non-linear model, an improvement of the computationaccuracy for determining the beat-to-beat stroke volume and/or thecardiac output is obtained. In particular, it is found to beadvantageous to approximate a pressure dependent volume V(p) of theaorta by the product of the cross-sectional area of the aorta and theeffective length Le of the aorta, the corresponding equation being givenby:

V(p)=A(p)Le,

wherein the cross-sectional area of the aorta A(p) may be approximatedby the arctangent model, given by the equation (1). Due to thisestimation a simple and reliable equation for the computation of thepressure-dependent arterial volume is obtained.

When the non-linear model (1) is applied to the Waterhammer model, oneobtains:

Z(w, pe)=Z _(o) +RZc/(R+Zc)

-   wherein-   Z is a total impedance of the aortic portion;-   Z_(o) is a characteristic impedance of the aorta;-   Zc is 1/jwC;-   W=2πf, with f the heart rate in Hz;-   R is a resistance;-   C is an aortic compliance, for example approximated by a non-linear    model.

It is found to be advantageous to iteratively determine the resistanceR. The resistance may also be referred to as a systemic vascularresistance. This can be performed in accordance with a followingalgorithm. First, the stroke volume is computed for R=1. From theresultant stroke volume a cardiac output is obtained by multiplicationby a heart rate. Second, R is computed from the mean pressure divided bycardiac output. Third, the entire stroke volume computation is repeatedagain and again with the recently obtained R until consecutive valuesdiffer by less than 1% or reaches a maximum number of iterations.Preferably, several iterations are carried out, for example five. Byiteratively adjusting a value of the resistor R an improvement of thecomputation accuracy is further obtained.

FIG. 2 presents in a schematic way an embodiment of a flowchart of thecomputer program according to the invention. The computer program 20according to the invention is arranged for determining beat-to-beatstroke volume and/or cardiac output based on at least one measurement ofan arterial pressure waveform. The computer program 20 may be stored asan executable file in a suitable memory of a computer. Alternatively,the computer program 20 may comprise a suitable number of executablesubroutines which are called in sequence during the execution of themethod as is discussed with reference to FIG. 1. The computer programmay be stored on a suitable carrier, like a disk. The computer program20 may also be integrated in measuring system arranged for determiningan arterial pressure data, for example a waveform, and for processingthe thus obtained data. In this case the computer program may comprisean instruction 22 for causing a suitable interface for collecting rawdata, notably from an invasive or a non-invasive device. A suitableexample of a computer-controlled non-invasive sensor is an inflatablecuff, discussed with reference to FIG. 4. Upon an event the measuringdata is collected, the computer program 20 follows to an instruction 24for processing said data. As a result the arterial waveform is accessed.After this, an instruction 26 is initiated causing a suitable processorto calculate compliance or an impedance of an aortic portion from anon-linear model. A suitable non-linear model may be accessed usinginstruction 27. The non-linear model 27 may comprise the arctangentmodel, which may be differentiated for obtaining the impedance or thecompliance of the aorta. Upon an event, this calculation is taken place,the compliance or impedance data may be fed into a per se known linearmodel, using the instruction 28. Suitable linear models, likeWaterhammer 28 a or Windkessel model 28 b have been discussed withreference to the method of the invention. Finally, the computer programcomprises instructions 29 a, 29 b for determining beat-to-beat volumeand/or cardiac output based on the compliance or impedance data and saidpulse contour model. It is possible that the beat-to-beat stroke volumeor cardiac output are computed based on different linear models and therespective results are averaged or suitably weighted.

FIG. 3 presents a schematic view of an embodiment of the systemaccording to the invention. The system 30 comprises a processor 31 and ameasurement unit 36, which may be arranged either to perform invasive ornon-invasive measurements of the arterial pressure data, notably awaveform. Data collected by the measurement unit are provided to theinput 33 of the processor 31. The processor 31 may further comprisestorage means 32 for storing a suitable non-linear model for computing acompliance or impedance in dependence of at least one measurement ofarterial pressure data. The processor 31 may further comprise acomputing unit 35 for using said compliance or impedance in a pulsecontour method for determining the beat-to-beat stroke volume and/orcardiac output based on the measured arterial pressure data. The storagemeans 32 may be arranged to store the per se known pulse contour models,like Waterhammer model and/or Windkessel model. Preferably, thecomputing means is arranged to use an arctangent model for saidnon-linear model. In this way a system is provided for determiningbeat-to-beat stroke volume and/or cardiac output based on themeasurement of an arterial pressure waveform with increased accuracycompared to prior art.

FIG. 4 presents a schematic view of an embodiment of a cuff for use inthe system of FIG. 3. The cuff 40 comprises a photoplethysmographarranged with an emitter of suitable radiation 46 and a detector of theradiation 45. In addition, the cuff 40 comprises an inflatable bladder48 provided with an air supply channel 42 for inflating the bladder andfor evacuating it. The cuff 40 is conceived to be arranged on a portionof the body, for example about a finger of a person, whereby a signalrelated to a blood flow in said portion is acquired using thephotoplethysmograph. During the data acquisition the inflatable bladderin pressurized so that all external pressure is applied to the portionbeing investigated. For this purpose the air supply channel 42 maycomprise a suitable fitting 41 for connecting to a pump, notably a gaspump.

Photoplethysmographs are known per se. An operational principle of thephotoplethysmograph is based on the fact that with each cardiac cyclethe heart pumps blood to the periphery of the body. A change in volumeof the arteries or arterioles caused by the pressure pulse of thesystolic wave is detected by illuminating the skin with a suitablelight, notably emitted from a Light Emitting Diode (LED) and thenmeasuring the amount of light either transmitted or reflected to asuitable detector, notably a photodiode. Alternatively, the emitter 46may be arranged to emit infrared radiation. Still alternatively, thephotoplethysmograph may be arranged in a transmissive set-up wherein thedetector 45 is arranged to measure a portion of radiation transmittedthrough a tissue of the patient. In case of a reflective set-up aportion of the radiation reflected from the tissue is detected. Eachcardiac cycle appears as a peak in a signal from thephotoplethysmograph. The shape of a signal waveform from thephotoplethysmograph differs from subject to subject, and varies with alocation and a manner in which the cuff is attached to the tissue. It isnoted that the photoplethysmograph can be attached to a great pluralityof areas on the human body, for example on a finger, on an ear, in anostril, on the temples of the head. The photoplethysmograph may even bearranged in a body cavity.

In the embodiment shown, the inflatable bladder 48 comprises a top-layer48″ conceived to be brought in contact with a portion of a body of aperson, notably with a finger, and a back-layer 48′ which may beattached to a flexible printed circuit 49. It is noted that theback-layer is preferably directly attached to the flexible printedcircuit 49 without using any additional adhesive inter-layers. Thetop-layer 48″ is arranged to be more flexible than the back-layer 48′.Due to this substantially only the top-layer of the inflatable bladderundergoes deformation in use, due to pressure within said bladder.Because a deformation of the back-layer 48′ might influence anemitter-detector geometry, it is advantageous to provide the inflatablebladder wherein substantially only the top-layer undergoes deformationill use. Due to this feature an increase in measurement accuracy isachieved. The back-layer 48′ may be attached to the top-layer 48″ by anysuitable technique, preferably a sealing method is used.

The inflatable bladder 48 may further comprise cut-away areas 48 a and48 b, wherein the emitter 46, notably a light emitting device (LED) anda detector 45, notably a photodiode are positioned, respectively. Theflexible printed circuit 49 may comprise corresponding cut-away areas 49a, 49 b for accommodating the emitter 46 and the detector 45. Theflexible printed circuit 49 may further comprise suitable blockers 53for shielding the emitter 46 and the detector 45 from interference withother light sources or detectors. Preferably, the detector 45 is alsoshielded from ambient light. Preferably, the blockers 53 comprise anopaque flexible material. A signal from the light detector 45 is pickedup by suitable electronic components (not shown) of the flexible printedcircuit 49. The flexible printed circuit 49 is electrically connectableto the cable 44 provided with a suitable electric connector 43. It ispossible that the cable 44 and the air supply 42 are housed in a jointhousing having sole outside connector 54. Preferably, the flexibleprinted circuit 49 further comprises a module 49 c for processing thesignal from the detector 45. Suitable signal processing steps maycomprise, but are not limited to, filtering, amplification, and/or thelike.

The cuff 40 may further comprise a sticker 50. A loop 51 and hook 47 maybe arranged to fasten the cuff about a finger of a person. Preferably,the top-layer 48″ is manufactured from a biocompatible material andextends substantially over the same length as the back layer 48′ orlabel 50. Due to this the label or back layer does not have to bemanufactured front a biocompatible material reducing the productioncosts of the cuff. The top-layer manufactured from a biocompatiblematerial may enhance possibility of a durable monitoring using the cuff,without causing irritation to a tissue of the person.

Preferably, a surface of the flexible printed circuit conceived to facethe tissue in use comprises an electrically conductive coating,preferably an electrically conductive and optically opaque andreflective coating. In accordance with this technical measure radiationimpinging the coating will be reflected back towards the tissue. Inaddition, a proper electrical shielding of the flexible printed circuitmay be enabled. The opacity of the flexible circuit materialadvantageously prevents the detector of the photoplethysmograph frominterference of ambient light with the photoplethysmograph. It is notedthat a usually envisage protective layer for covering metallic traces ofthe flexible printed circuit can be left out on the inner surface of theflexible printed circuit, which further reduces manufacturing costs ofthe cuff. Metal traces, notably copper traces, may be used in theflexible printed circuit to connect the electrical cable 44 to thecomponents of the flexible printed circuit, which makes wiringredundant, further decreasing manufacturing costs of the cuff accordingto the invention. The flexible printed circuit may be shaped with atail-end 49 d for relieving fastening strain to the wiring and the airtube in use.

While specific embodiments have been described above, it will beappreciated that the invention may be practiced otherwise than asdescribed. The descriptions above are intended to be illustrative, notlimiting. Thus, it will be apparent to one skilled in the art thatmodifications may be made to the invention as described in the foregoingwithout departing from the scope of the claims set out below.

What is claimed is:
 1. A non-transitory computer program productexecutable to cause a processor to carry out steps comprising: computinga compliance or impedance using a non-linear model and based on at leastone measurement of arterial pressure data; computing a stroke volume ora cardiac output using a pulse contour method and based on themeasurement of the arterial pressure data and the computed compliance orimpedance.
 2. A processor-based system including a processor configuredto carry out steps comprising: computing a compliance or impedance usinga non-linear model and based on at least one measurement of arterialpressure data; computing a stroke volume or a cardiac output using apulse contour method and based on the measurement of the arterialpressure data and the computed compliance or impedance.